Chapter 9, Problem 1IR

To determine

The supplementary and complement of the angle $27°$.

Answer to Problem 1IR

The supplementary and complement of the angle $27°$ is $\underset{\_}{153°}$ and $\underset{\_}{63°}$, respectively.

Explanation of Solution

Definition used:

Supplementary Angles:

Two angles that have a sum of $180°$ are called supplementary angles and each angle is the supplement of the other.

The angles $\angle R\text{ and }\angle \text{S}$ are supplementary if $m\angle R+m\angle S=180°$.

Complementary Angles:

Two angles that have a sum of $90°$ are called complementary angles and each angle is the complement of the other.

The angles $\angle R\text{ and }\angle \text{S}$ are complementary if $m\angle R+m\angle S=90°$.

Calculation:

The given angle is $27°$.

Evaluate the supplementary of $27°$ as follows.

$\begin{array}{c}\text{Supplement of }27°=180°-27°\\ =153°\end{array}$

Therefore, the supplementary of $27°$ is $\underset{\_}{153°}$.

Evaluate the complement of $27°$ as follows.

$\begin{array}{c}\text{Complement of }27°=90°-27°\\ =63°\end{array}$

Therefore, the complement of $27°$ is $\underset{\_}{63°}$.